Draisma, Jan; Horobet, Emil (2016). The average number of critical rank-one approximations to a tensor. Linear and multilinear algebra, 64(12), pp. 2498-2518. Taylor & Francis 10.1080/03081087.2016.1164660
|
Text
1408.3507.pdf - Accepted Version Available under License Creative Commons: Attribution-Noncommercial-No Derivative Works (CC-BY-NC-ND). Download (280kB) | Preview |
|
|
Text
The average number of critical rank one approximations to a tensor.pdf - Published Version Available under License Creative Commons: Attribution-Noncommercial-No Derivative Works (CC-BY-NC-ND). Download (692kB) | Preview |
Motivated by the many potential applications of low-rank multi-way tensor approximations, we set out to count the rank-one tensors that are critical points of the distance function to a general tensor v. As this count depends on v, we average over v drawn from a Gaussian distribution, and find formulas that relates this average to problems in random matrix theory.
Item Type: |
Journal Article (Original Article) |
|---|---|
Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |
UniBE Contributor: |
Draisma, Jan |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
0308-1087 |
Publisher: |
Taylor & Francis |
Language: |
English |
Submitter: |
Olivier Bernard Mila |
Date Deposited: |
31 Jul 2017 15:08 |
Last Modified: |
05 Dec 2022 15:05 |
Publisher DOI: |
10.1080/03081087.2016.1164660 |
ArXiv ID: |
1408.3507v2 |
BORIS DOI: |
10.7892/boris.99754 |
URI: |
https://boris.unibe.ch/id/eprint/99754 |
Actions (login required)
 |
Edit item |